Effects of positive jumps of assets on endogenous bankruptcy and optimal capital structure: Continuous- and periodic-observation models

TL;DR

This paper investigates how positive jumps in asset values influence optimal bankruptcy strategies and capital structure, comparing continuous and periodic observation models through numerical analysis.

Contribution

It introduces a comprehensive analysis of endogenous bankruptcy with positive jumps in asset processes, extending existing models to include periodic observation and two-stage optimization.

Findings

Optimal bankruptcy barrier depends on jump intensity and observation frequency.

Periodic observation models yield different strategies compared to continuous models.

Numerical results show sensitivity of firm decisions to asset jump characteristics.

Abstract

In this paper, we study the optimal capital structure model with endogenous bankruptcy when the firm's asset value follows an exponential L\'evy process with positive jumps. In the Leland-Toft framework \cite{LelandToft96}, we obtain the optimal bankruptcy barrier in the classical continuous-observation model and the periodic-observation model, recently studied by Palmowski et al.\ \cite{palmowski2019leland}. We further consider the two-stage optimization problem of obtaining the optimal capital structure. Detailed numerical experiments are conducted to study the sensitivity of the firm's decision-making with respect to the observation frequency and positive jumps of the asset value.